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arrow_back Find a formula in terms of $n$ for $\sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$. Simplify your answer fully.

by ♦ Platinum
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Find a formula in terms of $n$ for $\sum_{r=1}^{n}\left(3 r^{2}+r-2\right)$. Simplify your answer fully.

 

NB: You may find the following formulæ useful: $$ \sum_{r=1}^{n} r=\frac{n(n+1)}{2}, \quad \sum_{r=1}^{n} r^{2}=\frac{n(n+1)(2 n+1)}{6}, \sum_{r=1}^{n} r^{3}=\frac{n^{2}(n+1)^{2}}{4} $$

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